# Thread: z or t test ANOVA

1. ## z or t test ANOVA

I have a question about when I should use what...

ln (p/1-p) = B0 + B1 * age + B2 * civil status
n=100

Show with a statistical test that/if age and civil status affect the outcome of y.

B SE
Age -0,0632 0,0196
Civil status -0,0427 0,4545
Constant 2,8190 0,9335

So my question is if I should use a or b
a) z=B/SE =-0,0632/0,0196=-3,22 3,22>1,96 can show that it effects
=-0,0427/0,4545=-0,094 0,094<1,96 cant show that it effects

H0: B1=o B2=0
H1: B1≠0 B2≠0
b) t=b1-B1/sb1 =-0,0632-0/0,0196=-3,22
=-0,0427-0/0,4545=-0,094
tkrit= ?

2. ## Re: z or t test ANOVA

Hi emme1!

This is a multiple linear regression where you test the individual coefficients with a t-test.
Btw, ANOVA is not involved (there are no variances that are being analyzed).

For the first coefficient, you have:

H0: B1=0
H1: B1≠0

It's a t-distribution with n-3=100-3=97 degrees of freedom (generally df=n-p-1, where p is the number of parameters).

You get (slight modification of what you wrote):
t=(b1-0)/SEb1=-0,0632-0/0,0196=-3,22

Assuming an alpha of 5%, your critical t-value is t*=1,98.
(As you can see this is quite close to the 1,96 critical z-value you already had.)

Since t = -3,22 < -1,98, it follows that H0 can be rejected.

So yes, age has a significant effect on the outcome.

The method for the other coefficient is the same.

3. ## Re: z or t test ANOVA

Thanks a lot!!
and thank you for helping me with the df!

I just got the "correct answer" and they used the z-test.
hmm... When do you use the z-test like I wrote above?

4. ## Re: z or t test ANOVA

Hmm, the critical difference between a t-test and a z-test is knowledge about the standard deviation of the population parameter.

Wait, I'm just realizing that you are apparently testing proportions.
That is something that can be treated as having a known standard deviation.
The point being that the corresponding binomial distribution can be approximated by a normal distribution with a standard deviation that can be calculated.

To be honest, I'm not exactly sure of all the details, but it might be okay to do a z-test then.

Btw, as you've already seen, it matters not at all.
The critical values are very close, and the scores are way different.

5. ## Re: z or t test ANOVA

True!
So I guess both ways are correct?

I have seen both, but I just assumed that one of them was wrong... it's tricky

6. ## Re: z or t test ANOVA

From a practical point of view, both are just fine.

From a theoretical point of view, you should take a look at your notes, or your book.
It probably contains a worked example or something that shows exactly how you're supposed to do it... for a logistic regression in multiple variables.
(I'd tell you, but wikipedia does not appear to contain all the details.)